The view that Bayesian decision theory is only genuinely valid in a small world was asserted very firmly by Leonard Savage when laying down the principles of the theory in his path-breaking Foundations of Statistics. He makes the distinction between small and large worlds in a folksy way by quoting the proverbs ”Look before you leap” and ”Cross that bridge when you come to it”. You are in a small world if it is feasible always to look before you leap. You are in a large world if there are some bridges that you cannot cross before you come to them.

As Savage comments, when proverbs conflict, it is pro-verbially true that there is some truth in both—that they apply in different contexts. He then argues that some decision situations are best modeled in terms of a small world, but others are not. He explicitly rejects the idea that all worlds can be treated as small as both ”ridiculous” and ”preposterous” … Frank Knight draws a similar distinction between making decision under risk or uncertainty …

Bayesianism is understood [here] to be the philosophical principle that Bayesian methods are always appropriate in all decision problems, regardless of whether the relevant set of states in the relevant world is large or small. For example, the world in which financial economics is set is obviously large in Savage’s sense, but the suggestion that there might be something questionable about the standard use of Bayesian updating in financial models is commonly greeted with incredulity or laughter.

Someone who acts as if Bayesianism were correct will be said to be a Bayesianite. It is important to distinguish a Bayesian like myself—someone convinced by Savage’s arguments that Bayesian decision theory makes sense in small worlds—from a Bayesianite. In particular, a Bayesian need not join the more extreme Bayesianites in proceeding as though:

• All worlds are small.
• Rationality endows agents with prior probabilities.
• Rational learning consists simply in using Bayes’ rule to convert a set of prior
probabilities into posterior probabilities after registering some new data.

Bayesianites are often understandably reluctant to make an explicit commitment to these principles when they are stated so baldly, because it then becomes evident that they are implicitly claiming that David Hume was wrong to argue that the principle of scientific induction cannot be justified by rational argument …

Bayesianites believe that the subjective probabilities of Bayesian decision theory can be reinterpreted as logical probabilities without any hassle. Its adherents therefore hold that Bayes’ rule is the solution to the problem of scientific induction. No support for such a view is to be found in Savage’s theory—nor in the earlier theories of Ramsey, de Finetti, or von Neumann and Morgenstern. Savage’s theory is entirely and exclusively a consistency theory. It says nothing about how decision-makers come to have the beliefs ascribed to them; it asserts only that, if the decisions taken are consistent (in a sense made precise by a list of axioms), then they act as though maximizing expected utility relative to a subjective
probability distribution …

A reasonable decision-maker will presumably wish to avoid inconsistencies. A Bayesianite therefore assumes that it is enough to assign prior beliefs to as decisionmaker, and then forget the problem of where beliefs come from. Consistency then forces any new data that may appear to be incorporated into the system via Bayesian updating. That is, a posterior distribution is obtained from the prior distribution using Bayes’ rule.

The naiveté of this approach doesn’t consist in using Bayes’ rule, whose validity as a piece of algebra isn’t in question. It lies in supposing that the problem of where the priors came from can be quietly shelved.

Savage did argue that his descriptive theory of rational decision-making could be of practical assistance in helping decision-makers form their beliefs, but he didn’t argue that the decision-maker’s problem was simply that of selecting a prior from a limited stock of standard distributions with little or nothing in the way of soulsearching. His position was rather that one comes to a decision problem with a whole set of subjective beliefs derived from one’s previous experience that may or may not be consistent …

But why should we wish to adjust our gut-feelings using Savage’s methodology? In particular, why should a rational decision-maker wish to be consistent? After all, scientists aren’t consistent, on the grounds that it isn’t clever to be consistently wrong. When surprised by data that shows current theories to be in error, they seek new theories that are inconsistent with the old theories. Consistency, from this point of view, is only a virtue if the possibility of being surprised can somehow be eliminated. This is the reason for distinguishing between large and small worlds. Only in the latter is consistency an unqualified virtue.

at the time when evil liberals were supposedly forcing helpless bankers to lend into a housing bubble, leading to crisis, pretty much the very same people now claiming that it was all the government’s fault were vehemently denying that there was a bubble — and asserting that the only reason anyone even imagined that there might be a housing crisis looming was the malign impact of the biased liberal media.

As Adair Turner, chairman of the Financial Services Authority, argued in an important lecture this week, even greater attention needed to be paid to the “how” of monetary policy in exceptional times than to its targets. In particular, he argued, money creation was a legitimate and powerful tool, in such circumstances …

I agree with Lord Turner that the even more important question is how to make any policy effective. This, inevitably, raises questions about how monetary policy works in an environment of ultra-low interest rates. Lord Turner thinks the unthinkable: namely, monetary financing of the fiscal deficit. So should policy makers. They have to think afresh. If not now, when?

Or is it simply the case that studying cultural attitudes toward a phenomenon doesn’t really convey a solid understanding of how that phenomenon actually works? Is trying to understand debt by analyzing people’s attitudes toward debt somewhat akin to trying to understand the physics of a liquid-crystal display by studying the cultural effects of prime-time television?

In a recent lecture on the US recession – Robert Lucas gave an outline of what the New Classical school of macroeconomics today thinks on the latest downturn in the US economy and its future prospects.

Lucas starts by showing that real US GDP has grown at an average yearly rate of 3 per cent since 1870, with one big dip during the Depression of the 1930s and a big – but smaller – dip in the recent recession.

After stating his view that the US recession that started in 2008 was basically caused by a run for liquidity, Lucas then goes on to discuss the prospect of recovery, maintaining that past experience would suggest an “automatic” recovery, if the free market system is left to repair itself to equilibrium unimpeded by social welfare activities of the government.

As could be expected there is no room for any Keynesian type considerations on eventual shortages of aggregate demand discouraging the recovery of the economy. No, as usual in the New Classical macroeconomic school’s explanations and prescriptions, the blame game points to the government and its lack of supply side policies.

Lucas is convinced that what might arrest the recovery are higher taxes on the rich, greater government involvement in the medical sector and tougher regulations of the financial sector. But – if left to run its course unimpeded by European type welfare state activities -the free market will fix it all.

In a rather cavalier manner – without a hint of argument or presentation of empirical facts – Lucas dismisses even the possibility of a shortfall of demand. For someone who already 30 years ago proclaimed Keynesianism dead – “people don’t take Keynesian theorizing seriously anymore; the audience starts to whisper and giggle to one another” – this is of course only what could be expected. Demand considerations are simply ruled out on whimsical theoretical-ideological grounds, much like we have seen other neo-liberal economists do over and over again in their attempts to explain away the fact that the latest economic crises shows how the markets have failed to deliver. If there is a problem with the economy, the true cause has to be government.

While Greg Mankiw’s – one of the leading “New Keynesians” – only comment to this was a rather uninformative “I don’t always agree with Lucas, but I almost always find him thoughtful and thought-provoking,” Paul Krugman’s comment was more adroit:

[A]s is obvious to everyone but the hermetic inhabitants of the freshwater world, the attempt to explain business cycles in terms of rational expectations and frictionless markets has failed; and Keynesian economics continues to be very useful. But to concede that, to even consider the possibility that we’re in a demand-shortfall slump of the kind Keynes diagnosed, would be an incredible comedown for Lucas.

My rational expectation is that 30 years from now, no one will know who Robert Lucas was. John Maynard Keynes, on the other hand, will still be known as one of the masters of economics.

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